What is the van Hiele Model
of Geometric Thinking?

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While there is no specific grade level attachment to the van Hiele model of Geometric Thinking, when thinking about the Common Core State Standards, achieving Level 2: Informal Deduction, is an excellent goal for the end of 5th grade. 

Level 0:Visualization

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The most basic level of understanding geometric concepts is visualization. this level focuses on recognizing a "whole" shape and connecting that shape to a real-world object. For example, children might say that a square or rectangle looks like a window. Children at this level are not identifying any properties of shapes, but might be able to say "it is a circle/ it is not a circle," for instance.

Level 1: Analysis

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At Level 1, children start attaching properties to shapes, such as a triangle has three sides, or a square has four sides that are all the same length. Children at this level are able to fold and cut paper. 

Level 2: Informal Deduction

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Children at this level are able to find relationships between shapes and their properties. Completing a Venn Diagram, to determine similarities and differences of shapes and their properties, is a good activity to determine if children are at this level. 

Level 3: Deduction

Individuals at this level are able to generalize and use the properties of shapes to prove that a shape is indeed that shape. At this level, individuals are able to write proofs and understand the role of definitions. 

Level 4: Rigor

This final level is reserved for individuals who have a generalized understanding of geometric principles and different types of proofs. Individuals at this level might be majoring in mathematics at a collegiate level. 

Continue to Explore Kids Math Talk - Geometry for suggestions of Geometry talks, as well as links to professional learning resources.

Visit the Geometry Talk- Articles to Explore for links to more examples of the van Hiele Model of Geometric Thinking.